A surgical handpiece (20) with a rotating spindle (42) for receiving the couplinghead (54) of a surgical attachment (320) or a cutting accessory (48). A gear train(36) has plural drive heads (86, 92) that simultaneously rotate at differentspeeds. A clutch assembly (44) has pins (184) that move along the length of thespindle. The clutch assembly sets the position of the pins so they will engageone of the drive heads . The spindle rotates with the drive head with which the clutchpins are engaged.